Hi,
If x=3 and y = 6, then the third side will be 14-6-3 = 5.
Therefore, the three sides are 3,6,5.
We are counting the same triangle in the case x = 3 and y = 5.
When x = 3 and y = 5, the third side will be 14 - 3 - 5 = 6.
The triangle obtained has sides 3,6,5. Therefore, we will be double counting the same triangle.

Hi Swapnil,
These cases are taken into account.
If x = 3, y=6 , z=5 is same as x= 3, y=5 and z=6 (line 7)
If x=4, y=6, z=4 is same as x=y=4 and z=6 (line 7).
Hope this helps.

Hi Surya,

Let's take the two sides of the triangle as "y" and "14-(x+y)". Now we know that sum of any two sides is greater than the third side.

Hence y+14-(x+y)>x or y+14-x-y>x

or 14>2x or 7>x or x<7.

Hence from here we can conclude that x<7. Hope this helps. Thanks

Hi Kirti Garg,

In the solution to this question, the area of the regular pentagon is calculated using the standard formula, A= $$\dfrac{5}{4}\sqrt{\ 1+\dfrac{2}{\sqrt{\ 5}}}s^2$$

The formula is derived as follows: you will find that the height of each of the 5 triangles constituting the pentagon is equal to the $$\dfrac{side}{2\tan\left(\dfrac{180}{n}\right)}$$ = $$\dfrac{s}{2\tan\left(36\right)}$$

I hope this helps.